Journal of the ACM (JACM)
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Network Design with Weighted Players
Theory of Computing Systems - Special Issue: Symposium on Parallelism in Algorithms and Architectures 2006; Guest Editors: Robert Kleinberg and Christian Scheideler
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Weighted congestion games: price of anarchy, universal worst-case examples, and tightness
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Routing (un-) splittable flow in games with player-specific linear latency functions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
Hi-index | 0.00 |
We consider the problem of designing cost sharing protocols to minimize the price of anarchy and stability for a class of scheduling games. Here, we are given a set of players, each associated with a job of certain non-negative weight. Any job fits on any machine, and the cost of a machine is a non-decreasing function of the total load on the machine. We assume that the private cost of a player is determined by a cost sharing protocol. We consider four natural design restrictions for feasible protocols: stability, budget balance, separability, and uniformity. While budget balance is self-explanatory, the stability requirement asks for the existence of pure-strategy Nash equilibria. Separability requires that the resulting cost shares only depend on the set of players on a machine. Uniformity additionally requires that the cost shares on a machine are instance-independent, that is, they remain the same even if new machines are added to or removed from the instance. We call a cost sharing protocol basic, if it satisfies only stability and budget balance. Separable and uniform cost sharing protocols additionally satisfy separability and uniformity, respectively. For n-player games we show that among all basic and separable cost sharing protocols, there is an optimal protocol with price of anarchy and stability of precisely the n-th harmonic number. For uniform protocols we present a strong lower bound showing that the price of anarchy is unbounded. Moreover, we obtain several results for special cases in which either the cost functions are restricted, or the job sizes are restricted. As a byproduct of our analysis, we obtain a complete characterization of outcomes that can be enforced as a pure-strategy Nash equilibrium by basic and separable cost sharing protocols.